
It follows from (REF ) that the property (REF ) is preserved in time.
For regular solutions of NPNS it is shown in [1]}, [2]} that if \(c_i(0) \ge 0\) , then \(c_i(x, t)\)  remains nonnegative for \(t > 0\) . This property follows from (REF ) if \(c_i\)  are known to be sufficiently regular, and the same proof and result holds for the NPD equations.
